What should I do if Mac Disk Utility won't recognize my SSD?

There are too many unknowns here.

Is the SSD from the broken laptop the original Apple OEM SSD? Or a third party SSD?

What is the system firmware of the eBay laptop and version of macOS which was installed on it?

Did you carefully examine the SSD for any signs of damage?

Plus, were you able to confirm this eBay laptop even works before trying to install your SSD into the laptop?

Here is the OWC Envoy Pro Enclosure that is compatible with the proprietary Apple OEM SSD from MBPro Retina 2012 and Early-2013 laptops:

https://eshop.macsales.com/item/OWC/MAU3ENVOYPRO/

FYI, iCloud is not a backup although in this case it may have made things easier for accessing the data. iCloud is just a cloud based file syncing service. You make one catastrophic file edit on one device, and that catastrophic file edit is transferred to every other copy on every other device connected to iCloud.

People should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. It is very difficult to impossible to recover accidentally deleted data from an SSD after the Trash has been emptied. Plus there are a lot more new ways to permanently lose access to the data stored on the internal SSD of the recent Macs due to all the hardware, software, and security changes.

If your goal was to recover the data from the SSD, why not just put it into an external drive enclosure and access it from another computer?

The typical process for replacing an SSD (or HDD) is to install the new drive and format it in the Mac, then transfer the data from the old drive in an external enclosure.

Adding my usual plug for having at least one Time Machine backup, it's sad to see people have easily preventable issues. Back up your Mac with Time Machine - Apple Support

When your drive is a rotating magnetic drive, the magnetic regions on the drive live on through many, many different kinds is disasters, and can fairly often be rescued later, possibly by using extraordinary means.

The model Mac you have is one of the first with an SSD drive, and when SSD drives go wrong, for any one of many more reasons than rotating magnetic drives, the result is usually, "IT'S GONE".

The way forward is to make a backup copy of your files. "You don't need to backup everything, only the files you ever want to see again."

Utility drives have gotten cheap enough that there is NO EXCUSE for not having a Trusted backup drive on hand. Apple even includes their very good Utility for making backups, Time Machine, built into MacOS, for free.